lookat — (("interjection used to emphasise what follows" – Slanguage.))

get-up — outfit, general appearance. ((colloquial – Partridge HS.))

dinky — in the informal sense of "small and cute", not the American sense of "small and undesirable". ((OED.))

Bandbox – used for storing hats, etc

out of a bandbox — ((to look as if one came out of a bandbox: "to look extremely smart and neat" – OED.)) (("he is so neat and precise, so carefully got up in his dress and person, that he looks like some company dress, carefully kept in a bandbox" – Brewer 1898.))

little by little — ? reference to Frederic W. Farrar's 1858 novel "Eric, or, Little by Little" (("one of the most popular boys' books in Victorian Britain. It deals with the descent into moral turpitude of a boy at a boarding school".))

S.W.A.K. — (("'sealed with a kiss' on the back of an envelope" – Partridge HS.)) return — ? short for "return address".

ox-eyed — (("having large full eyes like those of an ox" – Webster 1913.))

scrapes — trouble. (("embarrassing or awkward predicament" – OED.))

bold particle — ? bold in an elementary way. ((bold: "forward, impudent" – PWJ 1910.)) This is the usual meaning of the word in Ireland: children, for instance, tend to be "bold" rather than "naughty". Particle — ? possibly fashioned on "elementary particle". It's an unusual usage of the word.

let on — (("betray, admit" colloquial – Farmer 1904.))

slice of the ignore — ? a serving of ignorance (in the IE sense of "rudeness". cf "ignorant" above.)

let him stew — leave him to worry on his own. ((stew in one's own juice: "be left vindictively or resentfully alone" – Farmer 1904.)) ((stew: "be left to suffer the natural consequences of one's own actions" – OED.))